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An “alligator spread” is a transaction is where the investor is unlikely to make much of a profit even if the markets move in the direction anticipated, primarily because the investor is “eaten alive” (as if by an alligator) by high commissions. The term ‘alligator spread” has been cited in print since at least February 1977.

InvestopediaDefinition of ‘Alligator Spread’
An unprofitable spread that occurs as a result of large commissions charged on the transaction, regardless of favorable market movements. An alligator spread is usually used in the options market to describe a collection of put and call options that may not be profitable.

27 February 1977, New York (NY) Times, “Commentary: Getting Alive in the Options Game” by Albert Haas Jr., pg. 101:
Cynics contend the most popular is the “alligator spread"-the broker makes a great deal of money, and the client gets eaten alive by commissions.

Google News Archive
11 April 1977, The Gazette (Montreal, Quebec), “Option trade booms in U.S.” by Ian Anderson, pg. 21, col. 3:
One jaded options player said the favorite options technique is the “alligator spread—the broker makes a great deal of money while the client gets eaten alive by commissions.”

Google BooksWords of Wall Street:
2,000 investment terms defined
By Allan H. Pessin and Joseph A. Ross
Homewood, IL: Dow Jones-Irwin
1983
Pg. 9:
ALLIGATOR SPREAD Slang for an option spread position that offers more in commission dollars to an account executive than to a client who accepts the risks of the spread. In effect, the client’s potential profit on the position is eaten up by the cost of the transaction.

Google BooksHigh Steppers, Fallen Angels, and Lollipops:
Wall Street Slang
By Kathleen Odean
New York, NY: Dodd, Mead
1988
Pg. 184:
A broker who blows a customer out after a point makes a commission at the customer’s expense, but the picture of “blowing out” surpasses the financial harm it describes. So, too, the facetiously named alligator spread, in which the brokers’ cimmissions eat up the customers’ profits, is hardly the equivalent of being devoured by an alligator.

Google BooksBarron’s Finance and Investment Handbook
By John Downes and Jordan Elliot Goodman
New York, NY: Barron’s Educational Series
1990
Pg. 186:
ALLIGATOR SPREAD spread in the options market that “eats the investor alive” with high commission costs. The term is used when a broker arranges a combination of puts and calls that generates so much commission the client is unlikely to turn a profit even if the markets move as anticpated.

Google BooksJonbull’s Stock Guide:
How to Invest Profitably in a Volatile Stock Market
By J. P. Obienugh
Victoria, BC: Trafford On Demand Pub
2010
Pg. 432:
Alligator spread – The term used to describe a spread in the options market that generates such a large commission that the client is unlikely to make a profit even if the markets move as the investor anticipated.